Simple Interest — Borrow low, lend high arbitrage: Prabhat borrows at 8% p.a. SI and lends the same sum to Ashish at 12% p.a. SI. If his profit in 2 years is Rs 320, how much did he borrow?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs. 4000
Explanation
Introduction / Context:Arbitrage under SI arises from lending at a higher rate than the borrowing rate. The net gain equals principal times the rate spread times time.
Given Data / Assumptions:
- Borrowing rate = 8% p.a.
- Lending rate = 12% p.a.
- Time = 2 years
- Profit = Rs 320
Concept / Approach:Profit = P * (rate spread) * t = P * (0.12 − 0.08) * 2 = 0.08 * P. Solve 0.08 * P = 320 for P.
Step-by-Step Solution:
0.08 * P = 320 ⇒ P = 320 / 0.08 = Rs 4000.Verification / Alternative check:
Interest received = 4000 * 12% * 2 = 960; paid = 4000 * 8% * 2 = 640; profit = 320 (matches).Why Other Options Are Wrong:
- 2000, 3000, 5000, 6000 do not yield a spread-based profit of 320 over 2 years.
Common Pitfalls:
- Using 12% − 8% = 2% instead of 4%; the spread is 4% per annum.
Final Answer:Rs 4000.